Method for realizing secure point multiplication in chips

Abstract

The invention discloses a method for realizing secure point multiplication in chips. The method comprises the following steps: 1, reading a scalar k and an elliptic curve point P for point multiplication operation; 2, generating a random bit sequence RandomBit with a duty ratio of 1 / N; 3, calculating a non-adjacent representation type (the formula is as shown in the specification) of the scalar k, wherein i belongs to {1, 3, 5, to 2w-1-1}, and calculating Pi=iP; 4, satisfying the condition that Q is equal to infinite; 5, for i from 1-1 to 0, carrying out repeated execution; 5.1, satisfying the condition that Q is equal to 2Q; 5.2, if the least bit of the RandomBit is 1, executing a pseudo operation DP, wherein RandomBit is bigger than or equal to 1, otherwise, if ki is not equal to 0 and greater than 0, Q is equal to Q+Pk1, and otherwise, Q is equal to Q-P-k1; and 6, returning to (Q). The method is capable of effectively resisting side channel attack, fault injection attack and template analysis attack so as to improve the security of chips, and is suitable for embedded equipment such as intelligent cards with computing resources constrained, such as financial cards and transportation cards using cryptographic security chips.

Description

technical field [0001] The invention relates to the field of safe execution of an elliptic curve public key cryptosystem in a chip, in particular to a method for implementing a secure point product in a chip. Background technique [0002] Since Miller and Koblitz independently proposed elliptic curve public key cryptography in 1985, elliptic curve public key cryptography (elliptic curve cryptosystem, referred to as ECC) has its unique advantages, such as fast calculation speed, small storage space, low bandwidth requirements, computing The few parameters and so on have aroused great concern of cryptographers. So far, ECC has not only been widely used in the field of information security, but also formed international standards (IEEEPI1363, ANSIX9, ISO / IEC and NIST, etc.) recognized by some international organizations as public key encryption standards. The core operation of the elliptic curve public key cryptosystem is the point multiplication operation, and the efficiency ...

AI Technical Summary

Problems solved by technology

Therefore, cryptographers have proposed many security implementation methods, such as adding pseudo-operations to balance point doubling and point addition, and some transform scalars so that point multiplication operations can resist simple power analysis, etc. However, due to the endless emergence of attack methods, the current implementation method resists one attack method but cannot be immune to another attack method

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